Certainly they do when they abruptly resign on the cusp of a big new strategic initiative and no reason is given for the move.

Just ask shareholders in Coinstar (NASDAQ:CSTR). Shares have tumbled more than 4% since the end of last week after the operator of those omnipresent Redbox video-rental kiosks said CEO Paul Davis is leaving — just as the company launches its highly anticipated online streaming service.

Yes, CEOs are overpaid by just about any yardstick or academic piece of research you care to cite, but considering that Davis’ unexpected and unexplained departure cost shareholders about $58 million in market value and counting, well … you can see how poor optics and communication can be a very expensive proposition.

In that sense, Davis was worth every penny. His salary and bonus came to about $1.4 million last year, or about 2% of the value of the decline in Coinstar’s market cap so far.

It would have been cheaper, at least in the short run, if he had stayed put.

But the selloff was almost certainly overdone — a knee-jerk reaction to unexpected news. That’s especially true since Davis is being replaced from within by the company’s CFO, which is key, since research shows that when it comes to top-level executives, skills do not translate from one area of expertise to another.

Indeed, that’s precisely why CEO compensation is so wildly inflated, according to one study.

The typical CEO makes something like 400 times as much money as a firm’s lowest-paid employee — up from 30 times a few decades ago. And much, if not all, of that compensation inflation can be attributed to inappropriate peer benchmarking, according to a paper by Charles Elson and Craig Ferrere at the University of Delaware’s Weinberg Center for Corporate Governance.

It turns out that boards pay CEOs bucketloads of cash because other CEOs are making bucketloads of cash — and you don’t want to lose your guy to another company just because he can get a bigger payday. Elson and Ferrere write:

“In setting the pay of their CEOs, boards invariably reference the pay of the executives at other enterprises in similar industries and of similar size and complexity. In what is described as ‘competitive benchmarking,’ compensation levels are generally targeted to either the 50th, 75th, or 90th percentile. This process is alleged to provide an effective gauge of ‘market wages’ which are necessary for executive retention.”

But it turns out the idea that there’s an efficient market for CEO talent is bunk. The skills of top managers are not fungible from industry to industry. Indeed, there’s no proof whatsoever that even the greatest Coinstar CEO would be equally effective at running a retail chain, car maker or widget manufacturer. Again, they write:

“There is no conclusive empirical evidence that outside succession leads to more favorable corporate performance, or even that good performance at one company can accurately predict success at another. Executive skills cannot pass the most basic test of generality: transferability.”

So while it’s good news that Coinstar promoted from within, anyone looking to hire Davis in the future would do well to make sure it’s in the same are of expertise. Otherwise, he will almost certainly be overpaid.

Which isn’t really all that counterintuitive. After all, no one would have expected the late Steve Jobs to be as good at selling, say, hamburgers as he was at running Apple (NASDAQ:AAPL). If anything, it appears that either Ford‘s (NYSE:F) Alan Mullaly — formerly of Boeing (NYSE:BA) — is either an exception to the rule, or the auto and aviation businesses aren’t as different as they would first appear.

Carefully orchestrated and well-telegraphed succession plans are needed when it comes to switching CEOs. Coinstar’s selloff is just the latest evidence of that. But when it comes to hiring new chief executives, it pays more to get someone who knows the field than just poaching a Wall Street rock star.

Shareholders should cast a skeptical eye the next time their company goes out of the industry to grab a headline name.

Ahem, Bob Nardelli, anyone?

As of this writing, Dan Burrows did not hold positions in any of the aforementioned securities.